Staggered Grid Higher Order Differential Numerical Simulation And Reverse Time Migration Imaging Studies. Well Seismic

As the urgent needs for oil and gas exploration and production and the technical improvements of down-hole source and receiver, cross-hole seismic has been becoming one important technology to structure accurate imaging and reservoir characterization and monitoring. The wave field of the multi-component cross-hole seismic data is terribly complicated, it is difficult to distinguish and separate the wave field each other, and the feature of anisotropy is prominent and extensive, so the conventional imaging method based on isotropy theory can't meet the needs of high accuracy and resolution imaging for cross-hole seismic reflection wave anymore. Aimed to this problem, this paper studies and discusses the staggered-grid finite-difference modeling of elastic equation and pre-stack, reverse-time migration for cross-hole seismic data.In this paper I derive completely the first-order coupled elastic equations of particle velocity and stress and the any order accurate time and space formulation of 2D staggered-grid, finite-difference scheme based on the research of previous author, analyze its stability and dispersion properties. The advantages of this scheme lie in its accuracy and stability for modeling any Poisson's ration materials, small grid dispersion and grid anisotropy and having no terms containing spatial derivatives. This method can be adopted to model the acoustic or elastic wave for both isotropic and transversely isotropic media with arbitrarily distributed material properties. For real cross-hole seismic data, this method models synthetic record that is coincident with the real cross-hole seismic records and recognizes the shear-wave birefringence of real cross-hole data.Reverse-time migration of pre-stacked cross-hole seismic date consists of three elements: (1) computation of the imaging condition; (2) extrapolation of the cross-hole seismic record wave field; and (3) application of the imaging condition. Excitation-time imaging condition, which is computed by nonlinear interpolation scheme for spherical-wave travel time, and high order accuracy staggered-grid, finite-difference scheme are used for the extrapolation and imaging of wave field. This imaging method abides by full wave equation and can obtain high accurate imaging section for arbitrary velocity distributions and is proved by testing with synthetic data that it has the desirable quality as follows: (1) Being applicable to the acoustic or...